{
  "abstract": "We prove that for every window $w$ of the form $w(x) = e^{-π|x|^2} h(x)$, where $h$ is a polynomial, there exists a uniformly discrete set of points $\\mathcal{S} \\subset \\mathbb R^{2d}$ such that the magnitude of the short-time Fourier transform $V_w f$ on $\\mathcal{S}$ determines every $f \\in L^2(\\mathbb R^d)$ up to a constant phase factor. The separation distance can be chosen independent of the degree of $h$ and proportional to the square root of the dimension. The proof combines a discrete norming inequality, based on a multidimensional Remez inequality and VC-dimension bounds, with tail estimates for the reproducing kernel. A formalization of our main result in Lean 4 is also provided.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.28341",
  "author_total": 4,
  "authors": [
    {
      "name": "Jaume de Dios Pont"
    },
    {
      "name": "Josef Greilhuber"
    },
    {
      "name": "Lukas Liehr"
    },
    {
      "name": "Mitchell A. Taylor"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/03at4c64y46yg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.28341",
  "fulltext_url": null,
  "id": "03at4c64y46yg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.28341",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CA"
    ],
    [
      "openalex",
      "2604|Mathematical Analysis and Transform Methods"
    ]
  ],
  "openalex": "W7214145195",
  "pdf_url": "https://arxiv.org/pdf/2609.28341",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/03at4c64y46yg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:00Z",
      "native_id": "2609.28341",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.28341"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Phase retrieval from a uniformly discrete point set",
  "title_text": "Phase retrieval from a uniformly discrete point set",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:00Z",
  "url": "https://research.draconitic.com/paper/03at4c64y46yg",
  "venue": "arXiv",
  "versions": []
}